Generally, a path for transmitting information may refer to a channel. When information is transmitted using a wired communication, the channel may be a transmission line transmitting the information, and when information is transmitted using a wireless communication, the channel may be electromagnetic waves transmitting the information.
Also, a process of storing information in a semiconductor memory device and reading the stored information from the semiconductor memory device may be the channel. The channel may be a temporal lapse from storing of the information until reading of the information, and may also be a physical path of storing information in the semiconductor memory device and reading the stored information from the semiconductor memory device.
While information is being transmitted via the channel, the information may be corrupted. The corrupted information may include an error and thus apparatuses and methods of detecting the error from the corrupted information and eliminating the detected error to restore initial information may be needed.
A process of adding error control codes (ECC) to initial information prior to transmitting the information to thereby generate transmission information may be referred to as ECC encoding. A process of receiving the transmission information and separating the ECC from the received transmission information to thereby restore the initial information may be referred to as ECC decoding.
Depending on channel characteristics, an error rate in the channel may be high. Generally, as the error rate increases, hardware complexity for ECC encoding and ECC decoding may increase in order to overcome the errors and achieve the desired performance.
In the case of the channel having the high error rate, a concatenated encoder concatenating a plurality of ECC encoders may be used. A process of restoring the initial information from the information generated by the concatenated encoder may be generally embodied using a concatenated decoder.
The concatenated decoder may be generally composed in a reverse order of the concatenated encoder. For example, when the concatenated encoder includes encoder A followed by encoder B, the concatenated decoder may include decoder B followed by decoder A.
ECC decoders and ECC decoding methods may be applied to memory devices that reduce decoding times.